The mass customization paradigm, in conjunction with high market demands, puts a significant burden on contemporary production systems to output a larger quantity of diversified parts. Consequently, production systems need to achieve even higher flexibility levels through physical and functional reconfigurability. One way of achieving these high levels of flexibility is by utilizing optimization of both scheduling and process planning. In this paper, the authors propose to solve an NP-hard integrated process planning and scheduling optimization problem with transportation constraints regarding one mobile robot. The proposed production environment includes four types of flexibilities (process, sequence, machine, and tool) that can be leveraged to optimize the entire manufacturing schedule. Three metaheuristic optimization algorithms are compared on the nine-problem benchmark based on the makespan metric. The proposed Mountain Gazelle Optimizer (MGO) is compared to the whale optimization algorithm and particle swarm optimization algorithm. The experimental results show that MGO achieves most best results, while it is highly comparable on the average best results.